Question: The sum of two angles is $86^\circ$. Angle 2 is $37^\circ$ smaller than $2$ times angle 1. What are the measures of the two angles in degrees?
Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 86}$ ${y = 2x-37}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${2x-37}$ for $y$ in the first equation. ${x + }{(2x-37)}{= 86}$ Simplify and solve for $x$ $ x+2x - 37 = 86 $ $ 3x-37 = 86 $ $ 3x = 123 $ $ x = \dfrac{123}{3} $ ${x = 41}$ Now that you know ${x = 41}$ , plug it back into $ {y = 2x-37}$ to find $y$ ${y = 2}{(41)}{ - 37}$ $y = 82 - 37$ ${y = 45}$ You can also plug ${x = 41}$ into $ {x+y = 86}$ and get the same answer for $y$ ${(41)}{ + y = 86}$ ${y = 45}$ The measure of angle 1 is $41^\circ$ and the measure of angle 2 is $45^\circ$.